Engineering Maths - Time and Work

11. A contract is to be completed in 46 days and 117 men were set to work, each working 8 hours a day. After 33 days, 4/7 of the work is completed. How many additional men may be employed so that the work may be completed in time, each man now working 9 hours a day?

  • Option : B
  • Explanation :
    of work is completed.
    Remaining work = 1-() =
    Remaining period = 46 - 33 = 13 days
    Less work, less men(direct proportion)
    Less days, more men(Indirect proportion)
    More hours/day, less men(Indirect proportion)
    work :
    Days 13:33 :: 117:x
    hrs/day 9:8
    × 13 × 9 × x = ()33 × 8 × 117
    x = (3 × 33 × 8 × 117) / (4 × 13 × 9)
    = 198 men
    So, additional men to be employed
    = 198 - 117 = 81
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12. A train traveling at 42 km/hr. passes a cyclist going in the same direction in 9 secs.; if cyclist had been going in the opposite direction, the train would have passed him in 5 secs. Length of the train is

  • Option : A
  • Explanation :
    Let L is length of train in km and x is speed of the cyclist, Then
    (i) 400L = 42 - x
    (ii) 720 L = 12 + x
    On adding, we get
    1120 L = 84
    ⇒ L = (84 x 1000)/1120 = 75m
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13. A man rows upstream 13 km. and downstream 28km taking 5 hr's each time. Velocity of the current is

  • Option : B
  • Explanation :
    13/Speed upstream = 5 and
    28/Speed downstream = 5
    ∴ Speed upstream = 13/5 km/hr
    and Speed downstream = 28/5 km/hr.
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14. A train overtakes 2 persons walking at 2 km/hr and 1 km/hr respectively in the same direction and completely passes them in 9 seconds and 10 seconds. Length of the train and its speed in km/hr respectively are

  • Option : D
  • Explanation :
    in each case, train has to travel its own length, to pass each man.
    If x km/hr is speed of the train, then
    Length = Relative speed x Time

    ∴ 9x - 18 = 10x - 40
    ⇒ x = 22km/hr.
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